Question

Suppose an astronaut can jump vertically with an initial velocity of 5 m/s. The time that it takes him to touch the ground is given by the equation 0 = 5t - 0.5at2. The time t is in seconds and the acceleration due to gravity a is in m/s2. How long will it take him to reach the ground if he jumps on Earth where a = 9.8 m/s2?

Answer 1

Answer:

$t=1.020s$

Step-by-step explanation:

Given Equation:

$5t-0.5at^{2} =0$

Actually the given equation is the 2nd equation of motion

i.e. $S =V_{i} t+0.5at^{2}$

where $S=0$ because the astronaut jumps on the earth

and initial velocity $V_{i}=5$

to find time $t$, put the given value of $a=9.8m/s^{2}$ in the given equation, we get

$5t-0.5(9.8)t^{2} =0\\t(5-4.9t)=0\\ \ dividing\ both\ sides\ by\ t\ we \ get\\ 5-4.9t=0\\4.9t=5\\t=\frac{5}{4.9}\\ t=1.020s$

it will take $t=1.020s$ to reach the ground if he jumps on the Earth